PSI - Issue 18

Luca Romanin et al. / Procedia Structural Integrity 18 (2019) 63–74 Author name / Structural Integrity Procedia 00 (2019) 000–000

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visible, and precipitates are more evident. By increasing the magnification, two types of precipitates could be classified by their shape, one developing in the direction of rolling and present only in the parent metal and the other one with a rounded shape and present both in the parent metal and in the FZ. The first one is in the order of 10 μm long while the latter is around 0.1 μm large. At the optical microscope no appreciable difference between the stress relived specimen (Test 3) and the as-received specimen could be noted in

the parent material. 5. Numerical model

A non-linear thermal transient analysis of the welding process has been performed. The fast motion and extremely fine focus of the heat source cause severe temperature gradients which have to be captured by a fine mesh and a small time-step. Even though a very fine mesh is not required in the thermal analysis, the more stringent requirements of the mechanical analysis constrain the mesh size. Taking advantage of geometrical and load symmetry only one plate has been modelled. A fixed time step of 0.05 s has been chosen when the heat source was moving inside the specimen. One of the objectives is to find the computational cheapest numerical model that could replicate experimental results. Thermal results are going to represent the input for a planned mechanical analysis, which is known to be more computational expensive. The thermal model has been validated using data of the specimen named “Test 3” in which two thermocouples have been inserted and a macrograph has been obtained from the middle section (Fig. 9). 5.1. Mesh 40000 ca. 3D linear elements have been utilized. The mesh has been graded both in the transversal and in the longitudinal direction to optimize the number of elements. On the symmetry plane, along the thickness, 8 elements of around 0.3 mm have been used as it can be seen in Figure 5. Moving far from the weld bead, gradually, only 4 elements along the thickness have been used.

Fig. 5. Cross section of the mesh

In the longitudinal direction the mesh is finer at the start and end of the weld seam while coarser in the middle where thermal condition can be considered quasi-stationary. For this reason, in the longitudinal direction, a parabolic bias has been imposed to have a finer mesh in the starting and ending region because of higher gradients due to the start and stop of the weld. Elements size ranges from 0.17 mm (welding start/end) to 0.77 mm in the middle, where the heat conduction could be considered stationary along the longitudinal direction. 5.2. Boundary and Initial conditions Heat loss have been taken into account considering thermal radiation, using the Stefan-Boltzman law, and an equivalent value for convection. Even if EBW was performed in vacuum, convection has been artificially introduced to take into account the heat dissipated by conduction from the clamps. Because of the small dimensions of the specimen the effect of the clamps is non negligible, the advantage of utilizing the convection coefficient is avoiding to model contact resistance which would have required a phenomenogical calibration and introduced another source of error. The value of the convection coefficient was empirically determined to be 10 W/m 2 , while the ambient temperature has been fixed to 25°C.